S0 = 0.005
d = 0.95 #m
d50 = 0.16 / (10**3) #mm
s = 2.65 #ماسه ای
# رسوبات بستر معلق میشود
ys = 0.15 #m 
rho_ys = 0.18 #%
rho = 2650 # kg / m^3
g = 9.81 # m^2 / s
mu = 0.001
rho_water = 1000 # kg / m^3
# rouse number? (w0/m^3)
# غلظت رسوبات از نقطه معلوم تا سطح آزاد؟

$V_* = \sqrt{gdsin(\theta)}$

from math import sqrt
V_star = sqrt(g * d * S0)
print('V* = %f'%V_star)

V* = 0.215865

$w_0 = - \sqrt{\frac{4gd_s}{3(\frac{24\mu}{\rho w_0d_s}+1.5)}(s-1)}$

from sympy.solvers import solve
from sympy import Symbol, sqrt
w_0 = Symbol('w_0')
javab = solve(w_0 - sqrt((4 * g * d50 * (s - 1))/(( (72 * mu) / (rho_water * w_0 * d50)+4.5))), w_0)
w_0 = - float(javab[0])
print("w0 = %f m/s"%w_0)

w0 = -0.019297 m/s

rouse_number = - w_0 / (0.4 * V_star)
from termcolor import colored
print(colored("rouse number = %f" %rouse_number, 'red'))

rouse number = 0.223486

def Cs (y):
    ys = 0.15
    rho_ys = 0.18
    Y = 0.95
    tavan = rouse_number
    soorat = (Y / y) - 1
    makhraj = (Y / 0.15) - 1
    return ((soorat / makhraj) ** tavan) * rho_ys
from numpy import arange
CS = []
YS = []
for y in arange(0.95, 0, -0.01):
    CS.append(Cs(y))
    YS.append(y)

import plotly.graph_objs as go
fig = go.Figure()
fig.add_trace(go.Scatter(x = CS, y = YS))
fig.update_layout(
    title="غلظت رسوبات",
    xaxis_title="C",
    yaxis_title="Y (m)",
    #legend_title="jaryan",
    font=dict(
        family="Courier New, monospace",
        size=18,
        color="RebeccaPurple"
    )
)